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Hyperscaling breakdown and Ising spin glasses: The Binder cumulant
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 492, p. 1838-1852Article in journal (Refereed) Published
Abstract [en]

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region. 

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 492, p. 1838-1852
Keywords [en]
Spin glasses, Ising model, Hyperscaling
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-145133DOI: 10.1016/j.physa.2017.11.101ISI: 000423495100151OAI: oai:DiVA.org:umu-145133DiVA, id: diva2:1187699
Available from: 2018-03-05 Created: 2018-03-05 Last updated: 2018-06-09Bibliographically approved

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Lundow, Per-Håkan

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CiteExportLink to record
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